The People's Kifah, or Struggle Against Hegemony, movement said in a statement that it carried out a detailed survey of Iraqi civilian fatalities during September and October 2003.
Its calculation was based on deaths among the Iraqi civilian population only, and did not count losses sustained by the Iraqi military and paramilitary forces.
The deputy general secretary and spokesperson of the movement told Aljazeera.net he could vouch for the accuracy of the figure.
"We are 100% sure that 37,000 civilian deaths is a correct estimate. Our study is the result of two months of hard work which involved hundreds of Iraqi activists and academics. Of course there may be deaths that were not reported to us, but the toll in any case could not be lower than our finding," said Muhammad al-Ubaidi.
The planning ministry is due to
hold a census in January 2005
"For the collation of our statistics we visited the most remote villages, spoke and coordinated with grave-diggers across Iraq, obtained information from hospitals, and spoke to thousands of witnesses who saw incidents in which Iraqi civilians were killed by US fire," he said.
Al-Ubaidi, a UK-based physiology professor, provided a detailed breakdown of the 37,000 civilian deaths for each governorate (excluding the Kurdish areas) relating to the period between March and October 2003:
Karbala and Najaf: 2263
Salah al-Din: 1797.
The People's Kifah said the process of data gathering stopped after one of the group's workers was arrested by Kurdish militias and handed over to US forces in October 2003. The fate of the worker remains unclear.
"I am taking this opportunity of talking to Aljazeera.net to request that the US occupation authorities reveal the whereabouts of the worker, who was arrested and then went missing. We are afraid he is being tortured the way Abu Ghraib prisoners were tortured," al-Ubaidi said.
"His name is Ramzi Musa Ahmad. He is a 32-year-old Iraqi engineer who was on his way to the Iraqi Kurdish governorate al-Sulaimania last October to fax me the information to Britain, because telephone services had not been restored in Baghdad."
According to al-Ubaidi: "The minibus in which Ahmad was travelling was stopped at a Kurdish checkpoint. He was arrested and handed over to US army."
As of now, there are no reliable estimates of total Iraqi civilian fatalities. The interim Iraqi government has not made available any statistics, while US occupation authorities in Iraq reportedly issued orders to the forensic medicine department not to talk to the media about the number of bodies it receives.
Liqa Makki, a political analyst, said it is widely known in Baghdad that Iraqi officials are prohibited from releasing any information about body count.
"I am seizing the opportunity of talking to Aljazeera.net to request that the US occupation authorities reveal the destiny of our worker, who was arrested and then disappeared"
"The director of forensic medicine department said publicly some months ago that his department was receiving 70 bodies a day. But he was reprimanded and a statement was published in the Iraqi press prohibiting the announcement of any kind of body count," Makki said.
The only serious independent attempt to collate war statistics is the Iraq Body Count Project, which involves both US and British academics. The project's website currently places Iraq's civilian toll at between 11,000 and 13,000.
The website has been criticised in some quarters for its tardiness in updating its figures. But Iraq Body Count Project says it is not a news portal and puts accuracy ahead of speed.
According to the Arab and western media, between 15,000 and 20,000 Iraqi civilians have perished since the launch of the invasion.
But some cast doubt on the figures, saying the number of Iraqi civilians who have died at the hands of the US army may never be known.
Iraq's interim government is preparing the first post-Saddam census in Iraq. It hopes that an accurate census will unearth long-buried facts about Iraq's wars.
The Planning Ministry issued instructions to Iraqis not to leave their homes on 12 October when 150,000 workers will be engaged in conducting the census.
The interim government says the census will be the last step before the general election scheduled for January 2005.
According to the last official census - conducted in 1997 - Iraq had a population of 24 million.